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SASMO 2020 Grade 4

Question 1

Platform scoring: start at 0; Q1–15 award 2 points each and Q16–25 award 4; wrong or blank answers score 0. Maximum 70. Official SASMO reference: start at 15; Section A correct +2, wrong −1, blank 0; Section B correct +4, wrong or blank 0. Official maximum 85.

What is the value of the following sum?

$2814+3700+4609+8211+9106-22900$
  1. 4450
  2. 4540
  3. 5540
  4. 5450
  5. None of the above

Question 2

If Gear A rotates anti-clockwise, which of the following options is true?

Question illustration

Assume the pictured gears mesh without slipping.
  1. Gears A and C rotate in opposite directions
  2. Four gears rotate in the same direction
  3. Gear E rotates clockwise
  4. Gear C rotates anti-clockwise
  5. None of the above

Question 3

In the fictional “Odd Island”, all the numbers contain only odd digits. The counting numbers are listed in increasing order: 1, 3, 5, 7, …, 19, 31, 33, … . What is the 55th counting number on the island?
  1. 99
  2. 101
  3. 197
  4. 199
  5. None of the above

Question 4

How many four-digit numbers are there such that adding 2020 to each still gives a four-digit number?
  1. 7020
  2. 6880
  3. 6980
  4. 7880
  5. None of the above

Question 5

In the grid below, the first row and first column contain the numbers from 10 to 19. Fill each empty cell by adding the topmost number in its column to the leftmost number in its row. For example, A = 17 + 14 = 31 and B = 19 + 18 = 37. What is the sum of all numbers in the completed grid?

Question illustration
  1. 745
  2. 725
  3. 145
  4. 135
  5. None of the above

Question 6

Each of 138 and 243 has digits whose product is 24. How many three-digit numbers have a product of digits equal to 24?
  1. 8
  2. 9
  3. 12
  4. 18
  5. None of the above

Question 7

December in a certain calendar year has exactly 5 Saturdays and 4 Sundays. On which day of the week does December 1 fall?
  1. Monday
  2. Tuesday
  3. Wednesday
  4. Thursday
  5. None of the above

Question 8

What is the missing number in the following pattern?

Question illustration

Pattern convention: use one simple rule depending on the number of sides and the number inside; a finite pattern can admit other rules.
  1. 5
  2. 10
  3. 16
  4. 20
  5. None of the above

Question 9

How many numbers are there in the list below?

$6\frac13,\ 7,\ 7\frac23,\ 8\frac13,\ \ldots,\ 30\frac13,\ 31$

Continue with the same constant increase shown by the consecutive listed terms.
  1. 25
  2. 26
  3. 38
  4. 37
  5. None of the above

Question 10

The five-digit number 25M48 is a multiple of 9. What digit does M represent?
  1. 9
  2. 8
  3. 7
  4. 6
  5. None of the above

Question 11

In the figure, ABCD and PQRS are rectangles. AD = PS = 6 cm and AB = PQ = 10 cm. Compare their shaded areas. Which statement is true?

Question illustration

Treat the drawn dividing lines and shared triangle bases as exact; do not estimate shaded area from dark pixel counts.
  1. The shaded areas of ABCD and PQRS are equal
  2. The shaded area of ABCD is greater
  3. The shaded area of ABCD is smaller
  4. Cannot be determined
  5. None of the above

Question 12

The time now is 16:56, and Archie’s 12-hour digital clock shows 4:56 P.M. Its digits are in increasing consecutive order. At 12:17 P.M. or A.M., the display shows 12:17 P.M. or A.M., respectively. How many minutes later will the clock again show digits in increasing consecutive order?

Read all displayed numeric digits, ignoring the colon and A.M./P.M. Single-digit hours have no leading zero.
  1. 507 minutes
  2. 458 minutes
  3. 467 minutes
  4. 407 minutes
  5. None of the above

Question 13

Ali has 80 candles. He lights one candle every day. He can recycle the wax of four used candles into one new candle. After how many days will he need to buy more candles?

Each candle lasts one day and leaves one usable wax portion. Recycled candles can be recycled again; no borrowing. Count the days fully supplied before a new candle must be bought.
  1. 80
  2. 130
  3. 132
  4. 133
  5. None of the above

Question 14

Among George, Helen and Irene, exactly one watched “Avengers”. George said, “Helen watched it.” Helen said, “I have not watched it.” Irene said, “I have not watched it.” If two of them lied, who watched the movie?
  1. George
  2. Helen
  3. Irene
  4. Impossible to determine
  5. None of the above

Question 15

Which option is the missing piece of the cube shown?

Question illustration

Question illustration

Compare the original shaded patterns and their orientation on all three faces.
  1. Piece A
  2. Piece B
  3. Piece C
  4. Piece D
  5. Piece E

Question 16

What is the value of $95\times37+95\times42+21\times95$?

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

Question 17

How many triangles are there in the figure below?

Question illustration

Count every triangle whose three straight sides are completely drawn, including larger composite triangles. Treat intended straight lines and common intersections as exact despite scan thickness.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

Question 18

I am thinking of a number. Add 8, multiply the sum by 8, subtract 8, then divide the difference by 8. The result is 80. What is the original number?

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

Question 19

The graph shows guests visiting the National Museum in the first six months of 2019. Horizontal lines are equally spaced. The total for January and May is 200 fewer than the June total. How many guests visited in all six months?

Question illustration

The bottom horizontal line is zero. Source graph labels Jan, Feb, Mar, Apr, May, Jun mean January through June.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

Question 20

The square is divided into four rectangles as shown. The sum of their perimeters is 72 cm. Find the side length of the square, in cm.

Question illustration

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.